Russian President Vladimir Putin called President Barack Obama on Friday to discuss a diplomatic resolution to the crisis in Ukraine, a gambit that could determine the trajectory of the biggest European security crisis in decades.

Both sides released descriptions of the call that differed on the details but agreed that the two countries’ foreign ministers would meet, an event that could take place as soon as next week.

The Putin call, which senior administration officials described as “frank and direct,” comes after both sides have steadily escalated the biggest confrontation between Russia and the U.S. since the end of the Cold War.

The U.S. and European Union have launched two rounds of sanctions, including some against prominent members of the Russian president’s inner circle, in retaliation for Russia’s annexation of Ukraine’s Crimea province.

Defying Western warnings, Russia has continued to reposition and augment its forces on the border of eastern Ukraine, according to U.S. officials, raising fears of a wider confrontation.

Russia’s Foreign Ministry on Friday dismissed the allegations as invented, saying that Western officials should “take a pain-reliever.”

The initiative came after Mr. Obama, ending an overseas trip that has focused heavily on sanctions against Russia, met with Saudi Arabia’s King Abdullah in Riyadh in an attempt to narrow their divisions over aid to Syrian rebels.

It remains unclear whether Mr. Putin’s offer was meant as a genuine prelude for talks or the groundwork for a new intervention. Some U.S. officials, skeptical of Mr. Putin’s approach, believe the buildup of forces on the border with Ukraine will give the Russian leader the option of launching another operation if he isn’t satisfied with the outcome of this diplomatic initiative. The troops may also be a bargaining chip in the talks since any invasion of eastern Ukraine likely would be much more difficult than Russia’s relatively bloodless conquest of Crimea.

The White House said U.S. Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov would meet to discuss a diplomatic proposal the two sides have been bouncing back and forth in recent weeks.

Mr. Obama in the hourlong call noted that “the Ukrainian government continues to take a restrained and de-escalatory approach to the crisis and is moving ahead with constitutional reform and democratic elections, and urged Russia to support this process and avoid further provocations, including the buildup of forces on its border with Ukraine,” according to the White House statement.

According to the Kremlin’s summary, Mr. Putin drew Mr. Obama’s attention to what he called the unpunished acts of extremists in Kiev and other regions of Ukraine. Mr. Putin also complained about what he called a blockade of the pro-Russian Transnistria region of Moldova, which borders Ukraine, injecting a new and potentially volatile element into the talks.

The Kremlin account could suggest Mr. Putin was seeking something like an internationally mandated protectorate over Ukraine, an idea Western capitals are unlikely to accept.

Russian soldiers stand near a tank outside a former Ukrainian military base near the Crimean capital of Simferopol. Agence France-Presse/Getty Images

Earlier Friday night, Russia’s ambassador to the United Nations renewed moscow’s calls for delaying the May 25 presidential elections to call a constitutional assembly first. Western officials fear such a delay would only allow Russia more time to apply pressure on Kiev to manipulate the outcome.

While the Crimean campaign has been hugely popular inside Russia, where Mr. Putin’s poll ratings—helped by propaganda in the state media—have jumped to the highest levels in years, the threat of isolation by the West has taken its toll on Russia’s already-stalling economy.

One senior administration official said the U.S. needed to hear back from the Russians “on substance before making a judgment on whether there is a serious opening” for diplomacy.

U.S. officials have voiced frustration with their dealings with Mr. Lavrov in particular in recent months. Some have described the Soviet-schooled diplomat as having little influence with Mr. Putin over Russian strategy in Ukraine. And some also worry that the Kremlin simply has been using him as diplomatic cover as they continue to deploy troops in and on the borders of Crimea.

On Friday’s call, the two presidents discussed a proposal, described by U.S. officials as “a working document” that Messrs. Kerry and Lavrov have been discussing on and off for weeks.

U.S. officials had hoped to develop joint approaches to tackle both Ukraine’s financial crisis and political problems. Mr. Kerry has also explored with Mr. Lavrov ways to address the Kremlin’s concerns that ethnic-Russians could be targeted by Kiev’s new government.

Earlier this month, Mr. Kerry passed to Mr. Lavrov documents outlining some of the steps that could be employed, according to senior U.S. officials.

These included drafting laws that would provide more autonomy to Ukraine’s regions; allowing for the continued promotion of the Russian language; and the deployment of U.N. and other monitors to protect vulnerable populations.

Mr. Kerry, however, told Mr. Lavrov during a string of meetings in Europe in recent weeks that such cooperation was contingent upon Moscow pulling out of Crimea and halting any other military incursions. U.S. officials said Mr. Lavrov refused to discuss the issue of pulling back Russian troops from Crimea during six hours of talks in London on March 14.

U.S. officials on Friday hadn’t decided how far Mr. Kerry would be willing to discuss future steps in Ukraine if Russia wasn’t agree to reverse its annexation.

U.S. officials said they were in contact with the Ukrainian government as the process of a diplomatic resolution with Russia proceeds. One possibility is that May elections in Ukraine could ease tensions by approving the status quo in Crimea. The U.S. has said the dispute should be decided by the government in Kiev, not Russia.

The Russian buildup along Ukraine’s eastern border has continued to worry U.S. defense officials who said they still didn’t know Mr. Putin’s intentions, a problem that has bedeviled Western policy makers since the crisis in Ukraine erupted.

As Mr. Putin’s impromptu call suggested, the movements could be designed to put pressure on Ukraine or gain diplomatic leverage. But the continuing movement of troops also means he now has the capability to enter eastern Ukraine, said a senior defense official.

“They are making adjustments for a possible incursion,” the senior official said. “You haven’t seen forces like this since the Russian war in Chechnya.”

U.S. officials said there are about 50,000 troops on the border and in Crimea currently. Although precise estimates of the size of the Russian force on the border vary, Moscow has massed far more troops than they used for the 2008 incursion into Georgia, according to U.S. officials.